A316147 Numbers, with digits in nondecreasing order, whose product of digits equals the number of digits times the sum of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 44, 159, 167, 235, 333, 1247, 1344, 2226, 11259, 11355, 111279, 111366, 112239, 112246, 112335, 1111377, 1111457, 1112337, 11111388, 11112267, 11113344, 11122236, 11222224, 111111399, 111111559, 111111666, 111112269

Offset: 1

Author

David A. Corneth, Jun 25 2018

Keywords

• nonn
• base
• easy

Comments

This sequence can be used to find terms of A064154 by permuting digits of terms of this sequence.

Crossrefs

Cf. A064154.

Programs

Mathematica

Union@ Flatten@ Reap[ Sow[0]; Do[ If[ FactorInteger[ nd s ][[-1, 1]] <= 7, Sow[ FromDigits /@ Reverse /@ Select[ IntegerPartitions[s, {nd}, Range[9]], Times @@ # == Length[#] Plus @@ # &]]], {nd, 18}, {s, 9 nd}]][[2, 1]] (* terms < 10^18, Giovanni Resta, Jul 18 2018 *)
dnoQ[n_]:=Module[{idn=IntegerDigits[n]},Min[Differences[idn]]>=0 && Times@@idn==Length[idn]Total[idn]]; Select[Range[0, 111112300],dnoQ] (* Harvey P. Dale, Aug 12 2021 *)

PARI

is(n) = my(d = digits(n)); vecsort(d) == d && prod(i=1, #d, d[i]) == #d * vecsum(d) \\ David A. Corneth, Jul 18 2018